Some entries from Londonderry Sentinel newspaper:
2 Oct.1838: On the 18th inst., the lady of Francis Rogan, Esq., M.D., of a daughter.
22 May 1841: On the 9th inst., the lady of Francis Rogan, Esq., M.D., of a son.
3 Dec.1842: On the 21st inst., the lady of Francis Rogan, Esq., M.D., of a son.
18 Aug.1854: On Sunday, the 13th inst., at his residence, St. Columb's Court, after a few days illness, Francis Rogan, Esq., M.D., of this City, aged 67 years.
12 Apr.1864: April 6, at Leven, Gourock, Margaret Erskine, relict of Francis Rogan, M.D., of Londonderry.
13 Sept.1834: In this City, on Saturday last, Mrs. Rogan, relict of the late Dr. Rogan, of Strabane.
27 Nov.1841: At Strabane, on Friday the 12th inst., Mr. Hugh Haliday.
30 Apr.1836: On Wednesday, the 27th inst., in Bishop street, Mrs. Haliday, aged 75 years. Her virtues as a wife, her precepts, example, and affection as a parent, and sincerity as a friend, were seldom to be equalled.
There are certainly lots of Rogans- an several of them medical men: H.G. Rogan & William Rogan both surgeons, R.N., Dr. Bernard Rogan, Dr. William Rogan, etc.
Don't know if they are of interest but if you want the rest of them let me know and I send them to you off list.